A free subalgebra of the algebra of matroids

This paper is an initial inquiry into the structure of the Hopf algebra of matroids with restriction-contraction coproduct. Using a family of matroids introduced by Crapo in 1965, we show that the subalgebra generated by a single point and a single loop in the dual of this Hopf algebra is free.Comment: 19 pages, 3 figures. Accepted for publication in the European Journal of Combinatorics. This version incorporates a few minor corrections suggested by the publisher

The Free product of Matroids

We introduce a noncommutative binary operation on matroids, called free product. We show that this operation respects matroid duality, and has the property that, given only the cardinalities, an ordered pair of matroids may be recovered, up to isomorphism, from its free product. We use these results to give a short proof of Welsh's 1969 conjecture, which provides a progressive lower bound for the number of isomorphism classes of matroids on an n-element set.Comment: 5 pages, 1 figure. Accepted for publication in the European Journal of Combinatorics. See also arXiv:math.CO/040902

A unique factorization theorem for matroids

We study the combinatorial, algebraic and geometric properties of the free product operation on matroids. After giving cryptomorphic definitions of free product in terms of independent sets, bases, circuits, closure, flats and rank function, we show that free product, which is a noncommutative operation, is associative and respects matroid duality. The free product of matroids $M$ and $N$ is maximal with respect to the weak order among matroids having $M$ as a submatroid, with complementary contraction equal to $N$. Any minor of the free product of $M$ and $N$ is a free product of a repeated truncation of the corresponding minor of $M$ with a repeated Higgs lift of the corresponding minor of $N$. We characterize, in terms of their cyclic flats, matroids that are irreducible with respect to free product, and prove that the factorization of a matroid into a free product of irreducibles is unique up to isomorphism. We use these results to determine, for K a field of characteristic zero, the structure of the minor coalgebra $\cal C$ of a family of matroids $\cal M$ that is closed under formation of minors and free products: namely, $\cal C$ is cofree, cogenerated by the set of irreducible matroids belonging to $\cal M$.Comment: Dedicated to Denis Higgs. 25 pages, 3 figures. Submitted for publication in the Journal of Combinatorial Theory (A). See arXiv:math.CO/0409028 arXiv:math.CO/0409080 for preparatory work on this subjec

Developing A Model Approximation Method and Parameter Estimates for Solid State Reaction Kinetics

The James S. Markiewicz Solar Energy Research Facility was built to research solar chemistry and currently being used to research the change in metal oxides such as iron or magnesium oxide that act as a medium for the production of hydrogen from water. This is significant because hydrogen can be used in vehicles equipped with appropriate fuel cells and due the decreased cost of producing hydrogen with this method. The shrinking core model which governs this process has proved difficult to solve due to the high number of unknown constants and its non-linearity. We detail in this work the implementation of less common heuristics, mainly Particle Swarm Optimization. This technique was used because of its wide unbiased search for the possible constants. The development and method we are using to solve these unknown constants will be shown

An application of linear species

AbstractCombinatorial operations on linear species are used in order to obtain, in a simple manner, the identity 11−αx=1+∑k⩾1 S(αk) xk1−xk′ where S(α; k) denotes the number of aperiodic words of length k over an alphabet with α elements. The cyclotomic identity follows as an immediate corollary

Discovery of Escherichia coli methionyl-tRNA synthetase mutants for efficient labeling of proteins with azidonorleucine in vivo

Incorporation of noncanonical amino acids into cellular proteins often requires engineering new aminoacyl-tRNA synthetase activity into the cell. A screening strategy that relies on cell-surface display of reactive amino acid side-chains was used to identify a diverse set of methionyl-tRNA synthetase (MetRS) mutants that allow efficient incorporation of the methionine (Met) analog azidonorleucine (Anl). We demonstrate that the extent of cell-surface labeling in vivo is a good indicator of the rate of Anl activation by the MetRS variant harbored by the cell. By screening at low Anl concentrations in Met-supplemented media, MetRS variants with improved activities toward Anl and better discrimination against Met were identified

Ro 15-4513 Antagonizes Alcohol-Induced Sedation in Mice Through aß¿2-type GABA(A) Receptors

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